Related papers: A Computational Interpretation of Context-Free Exp…
The neural architectures of language models are becoming increasingly complex, especially that of Transformers, based on the attention mechanism. Although their application to numerous natural language processing tasks has proven to be very…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
Explanations of cognitive behavior often appeal to computations over representations. What does it take for a system to implement a given computation over suitable representational vehicles within that system? We argue that the language of…
We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free…
Establishing whether language models can use contextual information in a human-plausible way is important to ensure their trustworthiness in real-world settings. However, the questions of when and which parts of the context affect model…
A problem is a multivalued function from a set of \emph{instances} to a set of \emph{solutions}. We consider only instances and solutions coded by sets of integers. A problem admits preservation of some computability-theoretic weakness…
Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Contextual equivalence is the de facto standard notion of program equivalence. A key theorem is that contextual equivalence is an equational theory. Making contextual equivalence more intensional, for example taking into account the time…
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…
Humans naturally interpret numbers non-literally, effortlessly combining context, world knowledge, and speaker intent. We investigate whether large language models (LLMs) interpret numbers similarly, focusing on hyperbole and pragmatic halo…
Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
Guarded Interaction Trees are a structure and a fully formalized framework for representing higher-order computations with higher-order effects in Rocq. We present an extension of Guarded Interaction Trees to support formal reasoning about…
Language models now provide an interface to express and often solve general problems in natural language, yet their ultimate computational capabilities remain a major topic of scientific debate. Unlike a formal computer, a language model is…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis…
One major problem in Natural Language Processing is the automatic analysis and representation of human language. Human language is ambiguous and deeper understanding of semantics and creating human-to-machine interaction have required an…
We present a complete reasoning principle for contextual equivalence in an untyped probabilistic language. The language includes continuous (real-valued) random variables, conditionals, and scoring. It also includes recursion, since the…